The LISREL10 program has a number of new statistical features.

Structural equation modeling (SEM) was introduced initially as a way of analyzing a covariance or correlation matrix. Typically, one would read this matrix into LISREL and estimate the model by maximum likelihood. If raw data was available without missing values, one could also use PRELIS first to estimate an asymptotic covariance matrix to obtain robust estimates of standard errors and chi-squares.

Modern structural equation modeling is based on raw data. With LISREL 10, if raw data is available in a LISREL data system file or in a text file, one can read the data into LISREL and formulate the model using either SIMPLIS syntax or LISREL syntax.

LISREL 10 contains fixes to all bugs reported by users of LISREL 9. The new LISREL features are summarized next.

## Multiple group analyses using a single data file

In practice, many multivariate data sets are observations from several groups. LISREL may be used to fit multiple group structural equation models to multiple group data. Traditional statistical methods such as Maximum Likelihood (ML), Robust Maximum Likelihood (RML), Weighted Least Squares (WLS), Diagonally Weighted Least Squares (DWLS), Generalized Least Squares (GLS) and Un-weighted Least Squares (ULS) are available for complete multiple group data while the Full Information Maximum Likelihood (FIML) method is available for incomplete multiple group data.

In previous versions of LISREL, the user was required to create separate data files for each group. Suppose that the groups to be analyzed consisted of data collected in eight countries, the implication is that eight datasets had to be created to fit a multiple group structural equation model. A new feature implemented in LISREL 10 allows researchers to use a single dataset that contains a group variable that can be defined by adding a

`$GROUPS=<group variable name> line anywhere in the syntax file.`

** **

**Models for grouped- and discrete-time survival data**

Models for grouped-time survival data are useful for analysis of failure time data when subjects are measured repeatedly at fixed intervals in terms of the occurrence of some event, or when determination of the exact time of the event is only known within grouped intervals of time. Additionally, it is often the case that subjects are observed nested within clusters (*i.e*., schools, firms, clinics), or are repeatedly measured in terms of recurrent events. In this case, use of grouped-time models that assume independence of observations is problematic since observations from the same cluster or subject are usually correlated. For data that are clustered and/or repeated, models including random effects provide a convenient way of accounting for association in correlated survival data.

Several authors have noted the relationship between ordinal regression models (using complementary log-log and logistic link functions) and survival analysis models for grouped and discrete time. In LISREL 10 a generalization of an ordinal random-effects regression model to handle correlated grouped-time survival data is implemented. This model accommodates multivariate normally-distributed random effects, and additionally, allows for a general form for model covariates.

**Models for ordinal outcomes and the proportional odds versus non-proportional odds assumption**

The term “ordinal” is applied to variables where the response measure of interest is measured in a series of ordered categories. Examples of such variables include Likert scales and psychiatric ratings of severity. Extensive work on the development of methods for the analysis of ordinal response data has been undertaken by numerous researchers. These developments have focused on the extension of methods for dichotomous variables to ordinal response data, and have been mainly in terms of logistic and probit regression models. The proportional odds model is a common choice for the analysis of ordinal data. In LISREL 10, it is possible to fit both proportional and non-proportional odds models to verify the proportional odds assumption using a chi-square difference test.

**P-value for C1 statistic under normality**

Modern structural equation modeling is based on raw data. With LISREL 10, if raw data is available in a LISREL data system file or in a text file, one can read the data into LISREL and formulate the model using either SIMPLIS syntax or LISREL syntax. It is no longer necessary to estimate an asymptotic covariance matrix with PRELIS and read this into LISREL. The estimation of the asymptotic covariance matrix and the model is now done in LISREL. One can also use the EM or MCMC multiple imputation methods in LISREL to fit a model to the imputed data.

Satorra & Bentler (1978) states that the asymptotic distribution of chi-square C1 is that of a linear combination of chi-squares with 1 degree of freedom, where the coefficients of the linear combination are the d (d = the degree of freedom) non-zero eigenvalues of UW_NNT, where U is defined in Satorra & Bentler (1978) and also in equation (45) in the document “New Features in LISREL 9” (available under “LISREL User & Reference Guides”) and W_NNT is an estimate of the asymptotic covariance matrix of the variances and covariance of the observed variables under non-normality, usually referred to as the ACM matrix.

LISREL 10 estimates the d eigenvalues and the p-value of the linear combination. Essentially, this makes the other chi-squares C2, C3, C4 and C5 less important, since they are based on approximations of the distribution using only the mean and variance of the eigenvalues.

**LISREL and PRELIS functionality**

Modern structural equation modeling is based on raw data. With LISREL 10, if raw data is available in a LISREL data system file or in a text file, one can read the data into LISREL and formulate the model using either SIMPLIS syntax or LISREL syntax. It is no longer necessary to estimate an asymptotic covariance matrix with PRELIS and read this into LISREL. The estimation of the asymptotic covariance matrix and the model is now done in LISREL. One can also use the EM or MCMC multiple imputation methods in LISREL to fit a model to the imputed data. If requested, LISREL will automatically perform robust estimation of standard errors and chi-square goodness of fit measures under non-normality. If the data contain missing values, LISREL will automatically use Full information maximum likelihood (FIML) to estimate the model. Alternatively, users may choose to impute the missing values by EM or MCMC and estimate the model based on the imputed data. Several new sections of the output are also included.

**Data conversion using stat/transfer**

The data import/export software has been upgraded from **Stat/Transfer** Version 13 to the most recently released Version 14.

**Selection of new features available Stat/Transfer Version 14**

Version 14 has added support for the following formats:

- Stata 15/MP
- BayesiaLab (Write Only)
- JSON-Stat (Read Only)

Version 14 has larger limits for:

- Excel Files > 4 GB
- SAS files > 32K variables
- Stata Files > 32K variables
- dBASE > 2GB

**FIML for ordinal and continuous variables**

LISREL 10 supports Structural Equation Modeling for a mixture of ordinal and continuous variables for simple random samples and complex survey data. The LISREL implementation allows for the use of design weights to fit SEM models to a mixture of continuous and ordinal manifest variables with or without missing values with optional specification of stratum and/or cluster variables. It also deals with the issue of robust standard error estimation and the adjustment of the chi-square goodness of fit statistic.

This method is based on adaptive quadrature and a user can specify any one of the following four link functions:

- Logit
- Probit
- Complementary Log-log
- Log-Log

**Three-level Multilevel Generalized Linear Models**

The collection of models called Generalized Linear Models (GLIMs) have become important, and practical, statistical tools. The basic idea of GLIMs is an adaption of standard regression to quite different kinds of data. The variables may be dichotomous, ordinal (as with a 5-point Likert scale), counts (number of arrest records), or nominal. The motivation is to tailor the regression relationship connecting the outcome to relevant independent variables so that it is appropriate to the properties of the dependent variable. The statistical theory and methods for fitting Generalized Linear Models (GLIMs) to survey data was implemented in LISREL 8.8.

Researchers from the social and economic sciences are often applying these methods to multilevel data and consequently, inappropriate results are obtained. The LISREL statistical module for the analysis of multilevel data allows for design weights. Two estimation methods, MAP (maximization of the posterior distribution) and QUAD (adaptive quadrature) for fitting generalized linear models to multilevel data are available. The LISREL Multilevel Generalized Linear models module (MGLIM) allows for a wide variety of sampling distributions and link functions.

The LISREL 10 MGLIM module also include zero-inflated Poisson and zero-inflated Negative-Binomial models and prints results for unit-specific and population-average estimates of the fixed effects.

**Four and Five-level Multilevel Models for continuous outcome variables**

Social science research often entails the analysis of data with a hierarchical structure. The need for statistical models that take account of the sampling scheme too is well recognized and it has been shown that the analysis of survey data under the assumption of a simple random sampling scheme may give rise to misleading results.

Multilevel models are particularly useful in the modeling of data from complex surveys. In order to address concerns regarding the appropriate analyses of survey data, the LISREL multilevel module for continuous data now also handles up to five levels and features an option for users to include design weights on levels 1, 2 , 3, 4 or 5 of the hierarchy.

**Filename extensions**

All LISREL syntax files have extension **.lis** (since LISREL 9, previously **.ls8**), all PRELIS syntax files have extension **.prl** (since LISREL 9, previously **.pr2**). The LISREL spreadsheet has been renamed LISREL data system file and has extension **.lsf** (since LISREL 9, previously **.psf**).

To ensure backwards compatibility, users can still run previously created syntax files using a **.psf** file, but to open an existing **.psf** file using the graphical user’s interface, the user has to rename it to **.lsf.**

**Running LISREL in batch mode**

Any of the LISREL programs can be run into batch mode by using a **.bat** file with the following script:

` "c:\program files (x86)\LISREL10\x64\MLISREL64_10" <Program Name> <Syntax file Name>`

where

`Program name`

= LISREL, PRELIS, MULTILEV, MAPGLIM or SURVEYGLIM, and `Syntax file Name`

= Name of syntax file (file extension included)